0
votes
0answers
13 views

Amplitude Spectrum, Nyquist Frequency, mixed/min/max wavelets

The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
0
votes
0answers
14 views

Evaluating an integral involving Haar scaling function

Let $\phi(t)$ denote the Haar scaling function, and let $\psi(t)$ be the corresponding wavelet. My problem is to evaluate the integral $I = \int_{t} \phi(t - 1/2) \frac{\partial \psi(t)}{\partial t} ...
2
votes
2answers
36 views

In which case should a wavelet transform be applied instead of a Fourier transform?

I was wondering what are the advantages (and possibly the drawbacks) of using a wavelet transform instead of a Fourier transform for the signal processing, are there simple examples to illustrate that ...
2
votes
1answer
82 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
1
vote
1answer
57 views

Denoise using wavelet transform

My mathematical class task is to de-noise a function using wavelet transform. I am to select a function $f(x)$ and noise function with zero-mean $n(x)$. I am to add noise like this: $$f_{noise}(x) = ...
2
votes
1answer
50 views

Daubechies wavelet

I have two question about Daubechies wavelet are they really orthogonality? for example daub4 has the support equal $[0-3]$, and for scale function we have must: $$ \int_0^3\phi(x-n)*\phi(x-m)dx ...
2
votes
2answers
107 views

Morlet's wavelet reconstruction formula

The CWT (continuous wavelet transform) of a signal $x(t)$ is $$X_w(a,b)=\frac{1}{\sqrt{|a|}} \int_{-\infty}^{\infty} x(t)\psi^{\ast}\left(\frac{t-b}{a}\right)\, dt$$ In order to reconstruct the ...
2
votes
1answer
99 views

compare wavelet and Fourier transform

i would like to compare each other wavelet and Fourier transform on given signal,let us consider following signal ...
1
vote
0answers
62 views

Output of wavelet transforms

I am working on a time sensitive computer science and fluid dynamics project that requires me to find applications of wavelet analysis. I know that at its core, a wavelet transform simply takes a ...
2
votes
0answers
103 views

An exercise. A property of the Fourier transform of wavelet

In the book "An Introduction To Wavelet Analysis" by David F. Walnut, there is, Exercise 7.45. Show that if $\psi(x)$ is a wavelet, then $\sum\limits_{j}{\left|\hat{\psi}(2^j\gamma)\right|^2} = 1$ ...
2
votes
1answer
198 views

A theorem about Lipschitz regularity and Fourier transform

How to prove that: A function $f$ is uniformly Lipschitz $\alpha$ over $\mathbb R$ if $$\int_{-\infty}^{+\infty}|\hat f(\omega)|(1+|\omega|^\alpha)d\omega<+\infty$$ A function $f$ is uniformly ...
11
votes
4answers
4k views

Difference between Fourier transform and Wavelets

While understanding difference between wavelets and Fourier transform I came across this point in Wikipedia. The main difference is that wavelets are localized in both time and frequency whereas ...
0
votes
0answers
104 views

Wavelet Transforms

I don't know as much as I would like to about Fourier analysis and I know almost nothing about wavelets. So just have a few conceptual questions to determine whether I should pursue their study or ...
0
votes
2answers
2k views

DFT and DWT difference?

what is the basic difference between the Discrete Fourier Transform and the Wavelet Transform ? and why does JPEG2000 preferred DWT over DCT or DFT ?
2
votes
1answer
129 views

Best way to find magnitude and phase of a specific frequency in an empirical time series…

I've a discrete, univariate time series, and I'm interested in to investigate a specific frequency component. Assume I'm interested in a frequency with a cycle-time of $f$ samples - and I need to get ...
5
votes
1answer
467 views

Wavelet Theory — where do I start?

I am in the process of implementing a Fixed-Point Fast Fourier Transform. The Fixed-Point FFT requires mathematical background in the area of wavelets and lifting schemes. What are good ...
7
votes
3answers
586 views

Decomposing a discrete signal into a sum of rectangle functions

Hello math@stackexchange community ! I have a simple question that seems to have a non trivial answer. Given a discrete one dimensional signal $w(x)$ defined in a finite range, and the boxcar ...
5
votes
2answers
431 views

Which time-frequency coefficients does the Wavelet transform compute?

(I asked this on Stack Overflow a while ago and didn't get a satisfying answer, so I'm trying again here.) The Fast Fourier Transform takes O(N log N) operations, while the Fast Wavelet Transform ...